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Math Help - arithmetic series

  1. #1
    Senior Member euclid2's Avatar
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    arithmetic series

    1. Find S20 for each arithmetic series listed below. A) 70 + 66 + 62 + 58 ...
      B) 3 + 9 + 15 + 21...
      C) 9 + 16 + 23 ...
      D) 3 + 2.5 + 2 + 1.5 ...

    Determine S20 for the arithmetic series with properties listed below. A) a = 2x and d = 5x ,
    B) t14= 46, and t19= 100
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by euclid2 View Post
    1. Find S20 for each arithmetic series listed below. A) 70 + 66 + 62 + 58 ...
      B) 3 + 9 + 15 + 21...
      C) 9 + 16 + 23 ...
      D) 3 + 2.5 + 2 + 1.5 ...

    Determine S20 for the arithmetic series with properties listed below. A) a = 2x and d = 5x ,
    B) t14= 46, and t19= 100
    recall the definition of an arithmetic series. these problems are pretty standard once you have that.

    an arithmetic series is one in which the terms are given by the formula

    a_n = a_1 + (n - 1)d

    where a_n is the nth term, a_1 is the first term, d = a_2 - a_1 = a_3 - a_2 = .... is the common difference, and n \ge 1 is an integer

    the sum of the first n terms, denoted by S_n is given by

    S_n = \frac {n(a_1 + a_n)}2 = \frac {n[2a_1 + (n - 1)d]}2

    thus, to find S_{20} we use

    S_{20} = \frac {20(2a_1 + 19d)}2

    you should be able to determine a_1 and d on your own for these problems
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